Meanwhile Wang Xiaolong, director general of the Foreign Ministry's department of worldwide economic affairs, said negotiations between Chinese and United States officials were making some progress.
They have also agreed to exchange visits at the appropriate time.
Exports of Fentanyl from China became the latest source of friction between the two countries as it has emerged as a new source of drug abuse in the U.S. in addition to heroin, resulting in large scale deaths of American youth.
The two sides would "step up negotiations" toward full elimination of all additional tariffs, Wang said.
"It's an incredible deal", Trump told reporters aboard Air Force One, on his way back to Washington.
Mr Trump had also said that if talks were unsuccessful, he would carry out a threat to hit the remaining $267b of annual Chinese exports to the USA with tariffs of 10-25 percent. Trump has threatened to go ahead with that and possibly add tariffs on $267 billion of imports if there is no progress in the talks.
Ahead of what was seen as the most important meeting of US and Chinese leaders in years, both sides said differences remained, and the outcome of the talks were uncertain.
Trump, as often in his diplomatic dealings, appears to consider his personal chemistry with Xi the most important factor in the success of the negotiations. "Only with cooperation between us can we serve the interest of both peace and prosperity", he said.
Xi also agreed to designate the drug fentanyl as a controlled substance, the White House said.
The White House said that Xi would consider approving a possible $44 billion deal for Qualcomm Inc.to purchase NXP Semiconductors NV if it's brought to him again.
In a release from White House Press Secretary Sarah Huckabee Sanders, Trump said, "This was an awesome and productive meeting with unlimited possibilities for both the United States and China".
Ms Merkel also said she hopes a meeting between the U.S. and Chinese leaders will help resolve trade tensions between the two countries.
Tyson Fury goes full Undertaker following THAT hook from Deontay Wilder
On the undercard, Jarrett Hurd defended his WBA and IBF 154-pound belts with a fourth-round stoppage of Jason Welborn. Welborn managed to get on the inside of Hurd, rocking him throughout the first three rounds of the bout.
Earlier in the day, the G20 leaders agreed to reform the World Trade Organisation, a big win for Trump who has heavily critisised it.
Joining other forecasters, economists at the Organisation for Economic Co-operation and Development last week downgraded their outlook for global economic growth next year to 3.5 percent from a previous 3.7 percent, citing the trade conflict, as well as political uncertainty.
But in a rhetorical olive branch to Trump, Xi pledged to do more to open up China's economy.
The state-run China Daily said that the Pacific powers could strike a deal in Buenos Aires but warned the United States against pushing too hard on technology.
U.S. officials insist that the American economy is more resilient to the tumult than China's, but they remain anxious of the economic effects of a prolonged showdown - as Trump has made economic growth the benchmark by which he wants his administration judges. Washington and Beijing have imposed tariffs on hundreds of billions of dollars on each other's imports after Trump began an effort to correct what he views as China's unfair commercial practices. Numerous countries have filed litigation at the WTO to contest the levies.
The U.S is unhappy with what it says is the WTO's failure to hold Beijing accountable for not opening up its economy as envisioned when China joined the body in 2001.
A Chinese official meanwhile said "consensus is steadily increasing" but differences remained.
It comes as International Monetary Fund (IMF) director Christine Lagarde urged G20 leaders to urgently de-escalate trade tensions and reverse tariff hikes.
"It's a consensus that meets numerous U.S.'s biggest objectives", said the official.
Trump-Xi Dinner Offers Chance to Avert Deeper U.S.
Leaders attending the G20 summit, however, applauded on Saturday after President Trump signed the joint communiqué at the close of the meeting in Argentina.
French President Emmanuel Macron reportedly delivered a strong message to MBS on Saudi journalist Jamal Khashoggi's brutal killing, and British Prime Minister Theresa May raised the issue of Khashoggi's murder during her meeting with the 33-year-old Prince, and "stressed the importance of ensuring that those responsible for the murder are held to account.".
The US president is prone to take kindly to others when he meets them face to face.